MathDB

Three natural numbers greater than or equal to

2

are written, not necessarily different, and from them a sequence is constructed using the following procedure: in each step, if the penultimate number written is

a

, the penultimate one is

b

and the last one is

c

, it is written

x

such that

x\cdot c=a+b+186.

Determine all the possible values of the three numbers initially written so that when the process continues indefinitely all the written numbers are natural numbers greater than or equal to

2

Problem Statement